Advertisements
Advertisements
Question
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
(A ∪ B)' = (A' ∩ B)'
Solution
A ∪ B = {1, 2, 3, 4} ∪ {3, 4, 5, 6}
= {1, 2, 3, 4, 5, 6}
∴ (A ∪ B)' = {7, 8, 9, 10} ...(1)
Now, A' = {5, 6, 7, 8, 9, 10} and
B' = {1, 2, 7, 8, 9, 10}
∴ A' ∩ B' = {5, 6, 7, 8, 9, 10} ∩ {1, 2, 7, 8, 9, 10}
= {7, 8, 9, 10} ...(2)
From (1) and (2), we get,
(A ∪ B)' = (A' ∩ B)'
APPEARS IN
RELATED QUESTIONS
If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A'∩B') = 5, find: n(A ∩ B)
If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A' ∩ B') = 5, find: n(A' ∩ B)
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
(A ∩ B)' = A' ∪ B'
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
A = (A ∩ B) ∪ (A ∩ B')
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
(A ∪ B) = (A − B) ∪ (A ∩ B) ∪ (B − A)
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
A ∩ (B ∆ C) = (A ∩ B) ∆ (A ∩ C)
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A'∩ B') = 5, find n(A ∩ B)
Solve the following inequality and write the solution set using interval notation
− 9 < 2x + 7 ≤ 19
Solve the following inequality and write the solution set using interval notation
x2 − x > 20
Solve the following inequality and write the solution set using interval notation
6x2 + 1 ≤ 5x
If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A ∪ B
If A = (–7, 3], B = [2, 6] and C = [4, 9] then find B ∪ C
If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A ∪ C
If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A ∩ B
If A = (–7, 3], B = [2, 6] and C = [4, 9] then find B ∩ C
If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A ∩ C
If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A' ∩ B
If A = (–7, 3], B = [2, 6] and C = [4, 9] then find B' ∩ C'
If A = (–7, 3], B = [2, 6] and C = [4, 9] then find B – C
For the set A = {a, b, c, d, e}, the correct statement is ______.
Answer the following:
If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write down the set A ∪ B
Answer the following:
If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write down the set A – B
Answer the following:
If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write down the set B ∩ C'
Answer the following:
If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write down the set A ∪ B ∪ C
Answer the following:
If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write down the set A ∩ (B ∪ C)
Answer the following:
If A = {1, 2, 3} and B = {2, 4}, state the elements of A × A, A × B, B × A, B × B, (A × B) ∩ (B × A)
Answer the following:
If A = {−1, 1} , find A × A × A
Let A, B, C be finite sets. Suppose that n (A) = 10, n (B) = 15, n (C) = 20, n (A ∩ B) = 8 and n (B ∩ C) = 9. Then the possible value of n (A ∪ B ∪ C) is ______.
Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Then ______.
